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Open Access Research Article

Approximately 2-absorbing and weakly approximately 2-absorbing sub-modules

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pp. 303–309Vol. 28Issue 2March 2025DOI: 10.47974/JDMSC-1852 Crossmark XML
Received:
07 May 2024
Published Online:
21 Mar 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1852
Pages:
303–309

Abstract

We outline the ideas of approximately 2-absorbing and weakly approximately 2-absorbing submodules and list the fundamental characteristics of these submodule classes. This is a generalization of prime and weakly prime sub-modules. Let A be a T-module and T a commutative ring. Weakly prime is the state in which a proper submodule U of A is when a, b ∈ T and m ∈ A, bam ∈ U implies that am ∈ U or bm ∈ U. When a, b within T, m in A and abm ∈ U then a proper submodule U of A is said to be approximately 2-absorbing (or weakly approximately 2-absorbing sub-modules). If a, b, ∈ T A m ∈ A, and abm ∈ U (resp.0≠abm ∈ U), then then a2 m ∈ N or b2 m ∈ N or a2 b2 ∈ (U:A).

Keywords

Subject Classifications

13A1513F05

References

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